It is common for a user to require high accuracy ranging for purposes such as positioning, navigation, or time transfer, and it is well known that accurate ranging requires radio frequency signals with large bandwidths. For example, satellite navigation systems such as GPS or GLONASS occupy several megahertz of spectrum in dedicated navigation bands. Systems for accurate ranging, such as time transfer or navigation systems, typically use a conventional high resolution ranging waveform. Examples of these conventional waveforms include short pulses, linear frequency modulated chirps, binary phase shift keyed signals, and binary offset carrier modulated signals.
All of these conventional waveforms require broad contiguous spectral bands. Outside of the dedicated navigation bands, which are already occupied by existing navigation signals, it can be extremely difficult or impossible to obtain allocation of broad, contiguous spectral bands that would be suitable for broadcasting conventional, high-accuracy ranging waveforms. Instead, the user is often constrained to operate in spectral bands where only a small number of noncontiguous bands are available, as is the case in the crowded VHF and UHF bands, for example.
One approach is to use a waveform that occupies available discontinuous spectral bands. However, until the present invention there was no known method of designing optimized discontinuous waveforms, and so this approach generally either provided ambiguous range estimates or provided accurate ranging only at unrealistically high Signal-to-Noise ratios (“SNR's”). Examples include the OMEGA radio navigation system (Pierce. 1965), which employed multiple pulsed sinusoids, but had ambiguities of hundreds of kilometers in the estimated location. Several works in the related areas of cognitive ranging (Celebi & Arslan. 2007; Gezici et. al., 2009) and radar (Cuomi. Piau. & Mahan, 1999; Levanon. 2000) have also addressed ranging using discontinuous spectral bands, and have suffered from similar ambiguity or SNR limitations.
What is needed, therefore, is a method of designing bandwidth efficient ranging waveforms that will provide accurate and unambiguous ranging at moderate to low SNR's.